Q. Two infinitely long parallel conducting wires A and B carry currents I and 2I, respectively, in the same direction. The wire A has uniform mass per unit length λ and lies on an insulated floor. The wire B is kept fixed at a height h above the floor. The minimum magnitude of h so that the wire A does not rise from the floor is: [g is the acceleration due to gravity and μ₀ is the permeability of free space.]
A) $\frac{4\mu_0I^2}{\pi\lambda g}$
B) $\frac{\mu_0I^2}{2\pi\lambda g}$
C) $\frac{\mu_0I^2}{\pi\lambda g}$
D) $\frac{2\mu_0I^2}{\pi\lambda g}$
Explanation
[Solution from source] Parallel currents attract, so B pulls A upward with force per unit length $\mu_0(I)(2I)/(2\pi h)=\mu_0I^2/(\pi h)$. A stays on the floor if this does not exceed λg, i.e. $h\ge\mu_0I^2/(\pi\lambda g)$. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.